2004年

I came up with the idea to build a small submarine after researching the internet and discovering the problems in which divers had to face in dangerous and time consuming tasks. The Remotely Operated Vessel (ROV) was designed to perform hull inspections on boats to look for hull damage and leakage of contaminates such as oil or other chemicals into the water. Search, rescue and recovery, are also common tasks which need to be carried out by the police when searching for objects and items. The ROV has been constructed at a reasonably low cost for submersing in depths down to 10 metres. It is remotely operated therefore needing a tether cable to link up between the computer and the vessel. I built a computer case-top from parts that I already had to eliminate the need for an expensive laptop. A program that I wrote in QBASIC interprets input data from the operator and sends out signals to the various operations on the vessel such as to dive, surface, propel, etc. The entire project consisted of five individual technology processes. Key processes such as Propulsion, Maneuverability, Dive & Surface capability, Imaging system, and the Control system. Each process required a cost effective and practical solution but still needing to function efficiently and be low maintenance. Through continuous testing and trial & error I feel I came up with the best possible solutions with the limited amount of time and money I had to spend. I wouldn’t have got as far as I have without the help and support from friends, family and local businesses. They helped with ideas and advice from time to time, help with funding, and the sponsorship of materials and tools. Now that the ROV is complete, I have been able to trial and test it in a swimming pool. Apart from discovering a few minor leaks in the hull and ‘bugs’ in the computer program, I was able to witness the success of the vessel under operation and find any improvements that could be done to make it work better in future. With further more tests at greater depths the ROV will soon be at the stage where it can perform hull inspections of boats and find lost objects and items underwater. I feel it has the opportunity to be a marketable device to underwater industries all over the world.

台灣地區高蹺?（Himantopus himantopus）的度冬族群出現月份是九月中旬至隔年四月，棲息地主要是在台灣西部沿海之鹽田、魚塭、沙質河口及少數內陸河川，而 1994年成立的台南四草野生動物保護區更是其在台灣的主要繁殖區。 本研究主要從2001年3月~2003年10月進行八掌溪嘉義市段高蹺?族群數量的調查，在 2001.12 月計數到最高數量約 1200 隻，2002.10 月有 1540 隻，連續兩個年度都是全國最高數量，分析環境因子及食物來源皆優於其他各沿海棲地。 在 2003 年 5 月至 9 月調查嘉義沿海高蹺?繁殖配對情形，在 5 月 24 日發現鰲鼓溼地巢數 25 個、幼鳥 14 隻，布袋七區鹽田巢數 9 個，顯示除了台南四草繁殖區外還有其他的繁殖地。 The winter residents of Black- winged Stilts in Taiwan appear in mid-September to next April. Their main habitats are the salt pans, water ponds, sandy river mouths and few inland rivers in western Taiwan. Furthermore, the “Taina Szu-Tao (四草) Wildlife Sanctuary” established in 1994 is their major breeding area. This research is the investigation of the amount of Black- winged Stilt in Pajhang River（八掌溪）, Chia-yi city（嘉義市） in 2001, Mar.~ 2003, Oct. The highest amount in 2001, Dec. is about 1200 and in 2002,Oct. is 1540. The amounts of these continuous two years are the highest in Taiwan. To analyze the reasons, the environment and food sources are better than other coastal habitats. In 2003, from May to September, the investigation of mating situation of Black-winged Stilt in Chia-yi coastal areas, twenty five nests and fourteen young birds in Ao-Ku(鰲鼓) wetland; nine nests in Pu-dai （布袋） seven salt pans are found on May 24th. It shows that there are other breeding areas except the breeding areas in Tainan Szu-Tao.

After reading “CKSH Communication 20 “, we are interested in Question 5 . We try to explain that in all the No. Crunches, whether we can put the numbers in the No. Crunches any certain position. We specify the question, according to the “Point Symmitry Homing” in mxn No. Crunches, to find the correlated characters of the rules. Finally, we find a “switch” – we can get the better way to rotate the numbers quickly by some programs.從「建中通訊解題」第20 期第5 題出發，本研究嘗試去解釋對所有的數字轉盤而言，是否能將其中的數字歸位到任意指定的位置？接下來將題目特殊化，藉由m× n 數字轉盤的「點對稱歸位」，尋找遊戲規則衍生出的相關性質。最後，利用研究出的性質找到一個「判斷式」可藉由程式設計，快速的找到較佳轉法。

我們研究的主題是曲率，且以高中所學的函數為主。雖然大學已有曲率公式，但我們將其表示成高中生較易了解的型式，並且以f(x) 的方式呈現。我們在函數曲線上取不共線三點，構成一個三角形，並求出此三角形的外接圓半徑。再將所取三點逼近，所求之半徑即為特定點的密切圓，也就是曲率半徑。而此曲率半徑的倒數，就是所求的曲率，同時我們將公式帶入高中各常見函數，以導出函數上各點曲率。;Our study is about curvature, especially about the fuctions we learn in senior high school. In university, there is a certain formula for curvature, but we hope to change it into a form that can be easily accepted by senior high school students, and express the formula with f(x), the symbol of functions. We pick three incollinear points from the curve of a function, making the three points into a triangle, and figure out the circumradius of this triangle. Then, we approximate the three points to one of them, and the circumradius will also be the radius of the osculating circle of the point. We define the radius as radius of curvature. The reciprocal of the radius of curvature will be the curvature. Then, we use the formula to figure out the curvature of the functions we learn in senior high school.

一個有3 個旋鈕，每個位置的號碼數分別是a、b、c 的密碼鎖，如果有兩個位置的數字正確就能打開，最少需要猜多少次才能保證打開這個鎖。在本論文中，我們將密碼鎖三個位置的號碼數分成：a＝b＝c＝n、a＝b＜c，a＝b＞c 和a＞b＞c 四個部份來討論。前兩部份的研究已經找到最少次數開鎖的方法 ，後兩部份則是給了一個演算法可求出開鎖次數的上界。If a combination lock with three rotate wheels can be opened when two wheels are adjusted to the correct numbers, then how many guesses does one need to make before he or she can actually open this lock? Let us say a , b and c respectively represents the numbers that should show on each wheel. In this paper, we divide the numbers into shown on the three wheels, and they are a = b = c = n , a = b c and a = b < c . The research on the first two combinations has already given us the method we can use to open he lock with the least number of trials. On the other hand, the latter two offer us an algorithm that can be uses to obtain the upper bound of tries needed to open the lock.

雙春海濱公園五年前規劃?紅樹林栽培區，透過學校向管理單位\r 申請調查。經由兩位學姊的協助下和特有生物保育中心所提供的資\r 料，結合目前調查和測試結果，對紅樹林成長過程中所產生的環境和\r 動物相改變，能有更詳細的探討。\r (一)、四種紅樹林品種以海茄苳成長最快繁殖力也比較強，其次是紅\r 海欖。\r (二)、紅樹林的成長伴隨環境因素的改變：\r 1. 砂土的攔截堆積量明顯增加。\r 2. 土壤的酸性因種植的紅樹林品種而有所改變。\r 3. 水質由於指標生物的出現間接可知有所改善。\r 4. 枯枝落葉等有機質增加提供食物網的基層能量。\r 5. 河道縮減導致漲潮時潮水漫流到低漥處。\r (三)、動物相的改變：\r 1. 以魚類魚苗、螺、貝和蟹類的種類和數量增加最明顯。\r 2. 養殖業中常出現的無脊椎寄生蟲數量增加，間接可以得知宿主\r 的數量也會有相對的增加。\r 3. 許多以往紅樹林調查未曾紀錄過的海鞘和星蟲均有新紀錄。\r Shuang-chun Coastal Park is planned as the planting region of mangrove during\r five years. The investigation is granted through our school’s application to the\r authorities concerned. Through the assistance of two senior alumni and the\r information offered by ESRI, combined with our investigation and the testing result,\r we can conduct a more detailed discussion about the changing phases of the\r environment and animals during the growing process of the mangrove.\r (I) Of the four species of mangroves, Avicennia marina grows the fastest with\r superior reproduction, and second comes Rhizophora mucronata.\r (II) The growth of mangrove accompanying the factor in the change of the\r environment:\r 1. The apparent increase in the sand piling\r 2. The variation of the soil acidity subject to the differences of mangroves\r 3. The quality of water is known to improve indirectly due to the existence of\r target living things.\r 4. Withered twigs and fallen leaves form organic substances to offer the bottom\r energy of the food chain.\r 5. The shrinkage of the river width leads to the overflowing of the low-lying area\r when the tide is on the flow.\r (III) The changes in the animal phase\r 1. The apparent increase in the species and number of fish fry, spiral shells, shells,\r and crabs.\r 2. The increase in the spineless parasites existing in the aquaculture, indirectly\r estimating the proportional increase in the hosts of the parasites.\r 3. A new record of tunicate and Sipunculus sp.，which were not recorded in the\r past many mangrove investigations.\r \r

這篇報告要探討下列的「轉沙發的問題」是否有解？有一個長方形的沙發(如圖一)，若要求每次只能以「四個頂點逆時針或順時針連續旋轉90 度」的方式轉動，請問當長寬具備何種關係時，沙發經數次轉動後，剛好可以「轉」到相鄰的位置(如圖一)，而且沙發坐人的正面方向仍保持不變呢？ 我們把原問題看成「平面座標上長方形旋轉的數學問題」，再利用「平面座標、三角函數、複數、複數的極式表示及向量」等數學工具，導出符合題目要求的方程式，最後證出下列的結果： 1.當長與寬比值為無理數時，此問題無解 2.當長與寬比值是最簡分數時；若分子為奇數，此問題無解 3.當長與寬比值為偶數時，此問題有解 In this paper we discuss the solution of rotating sofa problem as follows : The condition is : Merely allow to rotate the sofa several times by rotating 90 degrees clockwise or counterclockwise around the vertex. (maybe A, B, C, or D in Fig. 1) The question is : What’s the relationship between the length and the width of the sofa, if we request the sofa translated next to the original position with direction unchanged. (as shown in Fig. 1 with A’B’C’D’). We take this problem as a mathematical one of rotating a rectangle in plane coordinates. Then we derive the desired equations by using the tools of plane coordinates, trigonometric functions, complex number, polar form of complex number, and vector. Finally, we prove that： 1. When the ratio of length and width is irrational, the problem has no solution. 2. When the length of sofa is odd in the ratio of length and width, the problem has no solution. 3. When the ratio of length and width is even, the problem has solutions.